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Abstract

Spatio-temporally extended nonlinear systems often exhibit a remarkable
complexity in space and time. In many cases, extensive datasets of such systems are
difficult to obtain, yet needed for a range of applications. Here, we present a method to
generate synthetic time series or fields that reproduce statistical multi-scale features
of complex systems. The method is based on a hierarchical refinement employing
transition probability density functions (PDFs) from one scale to another. We address
the case in which such PDFs can be obtained from experimental measurements or
simulations and then used to generate arbitrarily large synthetic datasets. The validity
of our approach is demonstrated at the example of an experimental dataset of high
Reynolds number turbulence.